Low Complexity Successive Cancellation List Decoding of U-UV Codes

Constituted by BCH component codes and its ordered statistics decoding(OSD),the successive cancellation list(SCL)decoding of U-UV structural codes can provide competent error-correction performance in the short-to-medium length regime.However,this list decoding complexity becomes formidable as the decoding output list size increases.This is primarily incurred by the OSD.Addressing this challenge,this paper proposes the low complexity SCL decoding through reducing the complexity of component code decoding,and pruning the redundant SCL decoding paths.For the former,an efficient skipping rule is introduced for the OSD so that the higher order decoding can be skipped when they are not possible to provide a more likely codeword candidate.It is further extended to the OSD variant,the box-andmatch algorithm(BMA),in facilitating the component code decoding.Moreover,through estimating the correlation distance lower bounds(CDLBs)of the component code decoding outputs,a path pruning(PP)-SCL decoding is proposed to further facilitate the decoding of U-UV codes.In particular,its integration with the improved OSD and BMA is discussed.Simulation results show that significant complexity reduction can be achieved.Consequently,the U-UV codes can outperform the cyclic redundancy check(CRC)-polar codes with a similar decoding complexity.

Decoding topological XYZ^(2) codes with reinforcement learning based on attention mechanisms

Quantum error correction, a technique that relies on the principle of redundancy to encode logical information into additional qubits to better protect the system from noise, is necessary to design a viable quantum computer. For this new topological stabilizer code-XYZ^(2) code defined on the cellular lattice, it is implemented on a hexagonal lattice of qubits and it encodes the logical qubits with the help of stabilizer measurements of weight six and weight two. However topological stabilizer codes in cellular lattice quantum systems suffer from the detrimental effects of noise due to interaction with the environment. Several decoding approaches have been proposed to address this problem. Here, we propose the use of a state-attention based reinforcement learning decoder to decode XYZ^(2) codes, which enables the decoder to more accurately focus on the information related to the current decoding position, and the error correction accuracy of our reinforcement learning decoder model under the optimisation conditions can reach 83.27% under the depolarizing noise model, and we have measured thresholds of 0.18856 and 0.19043 for XYZ^(2) codes at code spacing of 3–7 and 7–11, respectively. our study provides directions and ideas for applications of decoding schemes combining reinforcement learning attention mechanisms to other topological quantum error-correcting codes.

Recurrent neural network decoding of rotated surface codes based on distributed strategy

Quantum error correction is a crucial technology for realizing quantum computers.These computers achieve faulttolerant quantum computing by detecting and correcting errors using decoding algorithms.Quantum error correction using neural network-based machine learning methods is a promising approach that is adapted to physical systems without the need to build noise models.In this paper,we use a distributed decoding strategy,which effectively alleviates the problem of exponential growth of the training set required for neural networks as the code distance of quantum error-correcting codes increases.Our decoding algorithm is based on renormalization group decoding and recurrent neural network decoder.The recurrent neural network is trained through the ResNet architecture to improve its decoding accuracy.Then we test the decoding performance of our distributed strategy decoder,recurrent neural network decoder,and the classic minimum weight perfect matching(MWPM)decoder for rotated surface codes with different code distances under the circuit noise model,the thresholds of these three decoders are about 0.0052,0.0051,and 0.0049,respectively.Our results demonstrate that the distributed strategy decoder outperforms the other two decoders,achieving approximately a 5%improvement in decoding efficiency compared to the MWPM decoder and approximately a 2%improvement compared to the recurrent neural network decoder.

Improved Segmented Belief Propagation List Decoding for Polar Codes with Bit-Flipping

Belief propagation list(BPL) decoding for polar codes has attracted more attention due to its inherent parallel nature. However, a large gap still exists with CRC-aided SCL(CA-SCL) decoding.In this work, an improved segmented belief propagation list decoding based on bit flipping(SBPL-BF) is proposed. On the one hand, the proposed algorithm makes use of the cooperative characteristic in BPL decoding such that the codeword is decoded in different BP decoders. Based on this characteristic, the unreliable bits for flipping could be split into multiple subblocks and could be flipped in different decoders simultaneously. On the other hand, a more flexible and effective processing strategy for the priori information of the unfrozen bits that do not need to be flipped is designed to improve the decoding convergence. In addition, this is the first proposal in BPL decoding which jointly optimizes the bit flipping of the information bits and the code bits. In particular, for bit flipping of the code bits, a H-matrix aided bit-flipping algorithm is designed to enhance the accuracy in identifying erroneous code bits. The simulation results show that the proposed algorithm significantly improves the errorcorrection performance of BPL decoding for medium and long codes. It is more than 0.25 d B better than the state-of-the-art BPL decoding at a block error rate(BLER) of 10^(-5), and outperforms CA-SCL decoding in the low signal-to-noise(SNR) region for(1024, 0.5)polar codes.

一套实用的企业应用分析框架CODE

随着企业信息化的深入,众多应用不再是“孤岛”,而是形成体系,应用间集成度越来越高,与业务的融合不断加深。在这种大趋势下,企业信息化在具体应用落地时要充分考虑其在企业体系中的定位,基于业务和技术环境找准发力点,才能最大化应用的价值。提出一套用于企业应用分析框架CODE,该分析框架由目标、业务上下文、系统上下文、领域、数据、分布、发展、接口、交互等要素构成,并充分考虑了企业环境的复杂性。经验证,该应用框架能够较好地完成应用分析,助力企业更好地进行应用建设。

Design of Serially Concatenated Two-Level Polar Coded Modulation System with Low-Complexity

Multilevel coding(MLC)is a commonly used polar coded modulation scheme,but challenging to implement in engineering due to its high complexity and long decoding delay for high-order modulations.To address these limitations,a novel two-level serially concatenated MLC scheme,in which the bitlevels with similar reliability are bundled and transmitted together,is proposed.The proposed scheme hierarchically protects the two bit-level sets:the bitlevel sets at the higher level are sufficiently reliable and do not require excessive resources for protection,whereas only the bit-level sets at the lower level are encoded by polar codes.The proposed scheme has the advantages of low power consumption,low delay and high reliability.Moreover,an optimized constellation signal labeling rule that can enhance the performance is proposed.Finally,the superiority of the proposed scheme is validated through the theoretical analysis and simulation results.Compared with the bit interleaving coding modulation(BICM)scheme,under 256-quadrature amplitude modulation(QAM),the proposed scheme attains a performance gain of 1.0 dB while reducing the decoding complexity by 54.55%.

Text-and-Timbre-Based Speech Semantic Coding for Ultra-Low-Bitrate Communications

To address the contradiction between the explosive growth of wireless data and the limited spectrum resources,semantic communication has been emerging as a promising communication paradigm.In this paper,we thus design a speech semantic coded communication system,referred to as Deep-STS(i.e.,Deep-learning based Speech To Speech),for the lowbandwidth speech communication.Specifically,we first deeply compress the speech data through extracting the textual information from the speech based on the conformer encoder and connectionist temporal classification decoder at the transmitter side of Deep-STS system.In order to facilitate the final speech timbre recovery,we also extract the short-term timbre feature of speech signals only for the starting 2s duration by the long short-term memory network.Then,the Reed-Solomon coding and hybrid automatic repeat request protocol are applied to improve the reliability of transmitting the extracted text and timbre feature over the wireless channel.Third,we reconstruct the speech signal by the mel spectrogram prediction network and vocoder,when the extracted text is received along with the timbre feature at the receiver of Deep-STS system.Finally,we develop the demo system based on the USRP and GNU radio for the performance evaluation of Deep-STS.Numerical results show that the ac-Received:Jan.17,2024 Revised:Jun.12,2024 Editor:Niu Kai curacy of text extraction approaches 95%,and the mel cepstral distortion between the recovered speech signal and the original one in the spectrum domain is less than 10.Furthermore,the experimental results show that the proposed Deep-STS system can reduce the total delay of speech communication by 85%on average compared to the G.723 coding at the transmission rate of 5.4 kbps.More importantly,the coding rate of the proposed Deep-STS system is extremely low,only 0.2 kbps for continuous speech communication.It is worth noting that the Deep-STS with lower coding rate can support the low-zero-power speech communication,unveiling a new era in ultra-efficient coded communications.

Soft Decoding Scheme of Convolution Code Combined with Huffman Coding

This paper proposes a modification of the soft output Viterbi decoding algorithm (SOVA) which combines convolution code with Huffman coding. The idea is to extract the bit probability information from the Huffman coding and use it to compute the a priori source information which can be used when the channel environment is bad. The suggested scheme does not require changes on the transmitter side. Compared with separate decoding systems, the gain in signal to noise ratio is about 0 5-1.0 dB with a limi...

Efficient construction and encoding of QC-LDPC codes by cyclic lifting of protographs

Quasi-cyclic low-density parity-check （QC-LDPC） codes can be constructed conveniently by cyclic lifting of protographs. For the purpose of eliminating short cycles in the Tanner graph to guarantee performance, first an algorithm to enumerate the harmful short cycles in the protograph is designed, and then a greedy algorithm is proposed to assign proper permutation shifts to the circulant permutation submatrices in the parity check matrix after lifting. Compared with the existing deterministic edge swapping （DES） algorithms, the proposed greedy algorithm adds more constraints in the assignment of permutation shifts to improve performance. Simulation results verify that it outperforms DES in reducing short cycles. In addition, it is proved that the parity check matrices of the cyclic lifted QC-LDPC codes can be transformed into block lower triangular ones when the lifting factor is a power of 2. Utilizing this property, the QC- LDPC codes can be encoded by preprocessing the base matrices, which reduces the encoding complexity to a large extent.

Error concealment in pixel based Wyner-Ziv video coding

In the Wyner-Ziv(WZ) video coding paradigm, a virtual correlation channel is assumed between the quantized source and the side information(SI) at the decoder, and channel coding is applied to achieve compression. In this paper, errors caused by the virtual correlation channel are addressed and an error concealment approach is proposed for pixel-based WZ video coding. In the approach, errors after decoding are classified into two types. Type 1 errors are caused by residual bit errors after channel decoding, while type 2 errors are due to low quality of SI in part of a frame which causes SI not lying within the quantization bin of a decoded quantized pixel value. Two separate strategies are respectively designed to detect and conceal the two types of errors. Simulations are carried out and results are presented to demonstrate the effectiveness of the proposed approach.

Joint Source-Channel Decoding of EVRC Speech Encoder Using Residual Redundancy

The enhanced variable rate codec (EVRC) is a standard for the 'Speech ServiceOption 3 for Wideband Spread Spectrum Digital System,' which has been employed in both IS-95cellular systems and ANSI J-STC-008 PCS (personal communications systems). This paper concentrateson channel decoders that exploit the residual redundancy inherent in the enhanced variable ratecodec bitstream. This residual redundancy is quantified by modeling the parameters as first orderMarkov chains and computing the entropy rate based on the relative frequencies of transitions.Moreover, this residual redundancy can be exploited by an appropriately 'tuned' channel decoder toprovide substantial coding gain when compared with the decoders that do not exploit it. Channelcoding schemes include convolutional codes, and iteratively decoded parallel concatenatedconvolutional 'turbo' codes.

Erasure-Correction-Enhanced Iterative Decoding for LDPC-RS Product Codes

Low-density parity-check(LDPC)codes are widely used due to their significant errorcorrection capability and linear decoding complexity.However,it is not sufficient for LDPC codes to satisfy the ultra low bit error rate(BER)requirement of next-generation ultra-high-speed communications due to the error floor phenomenon.According to the residual error characteristics of LDPC codes,we consider using the high rate Reed-Solomon(RS)codes as the outer codes to construct LDPC-RS product codes to eliminate the error floor and propose the hybrid error-erasure-correction decoding algorithm for the outer code to exploit erasure-correction capability effectively.Furthermore,the overall performance of product codes is improved using iteration between outer and inner codes.Simulation results validate that BER of the product code with the proposed hybrid algorithm is lower than that of the product code with no erasure correction.Compared with other product codes using LDPC codes,the proposed LDPC-RS product code with the same code rate has much better performance and smaller rate loss attributed to the maximum distance separable(MDS)property and significant erasure-correction capability of RS codes.

A simplified decoding algorithm for multi-CRC polar codes

Polar codes represent one of the major breakthroughs in 5G standard,and have been proven to be able to achieve the symmetric capacity of binary-input discrete memoryless channels using the successive cancellation list(SCL)decoding algorithm.However,the SCL algorithm suffers from a large amount of memory overhead.This paper proposes an adaptive simplified decoding algorithm for multiple cyclic redundancy check(CRC)polar codes.Simulation results show that the proposed method can reduce the decoding complexity and memory space.It can also acquire the performance gain in the low signal to noise ratio region.

Relative-Residual-Based Dynamic Schedule for Belief Propagation Decoding of LDPC Codes

Two Relative-Residual-based Dynamic Schedules(RRDS) for Belief Propagation(BP) decoding of Low-Density Parity-Check(LDPC) codes are proposed,in which the Variable code-RRDS(VN-RRDS) is a greediness-reduced version of the Check code-RRDS(CN-RRDS).The RRDS only processes the variable(or check) node,which has the maximum relative residual among all the variable(or check) nodes in each decoding iteration,thus keeping less greediness and decreased complexity in comparison with the edge-based Variable-to-Check Residual Belief Propagation(VC-RBP) algorithm.Moreover,VN-RRDS propagates first the message which has the largest residual based on all check equations.For different types of LDPC codes,simulation results show that the convergence rate of RRDS is higher than that of VC-RBP while keeping very low computational complexity.Furthermore,VN-RRDS achieves faster convergence as well as better performance than CN-RRDS.

A New Region-of-interest Coding Method to Control the Relative Quality of Progressive Decoded Images

Based on the ideas of controlling relative quality and rearranging bitplanes, a new ROI coding method for JPEG2000 was proposed, which shifts and rearranges bitplanes in units of bitplane groups. It can code arbitrary shaped ROI without shape coding, and reserve almost arbitrary percent of background information. It also can control the relative quality of progressive decoded images. In addition, it is easy to be implemented and has low computational cost.

Efficient Soft-Decision Maximum-Likelihood Decoding of BCH Code in the GNSS

Soft-decision decoding of BCH code in the global navigation satellite system( GNSS) is investigated in order to improve the performance of traditional hard-decision decoding. Using the nice structural properties of BCH code,a soft-decision decoding scheme is proposed. It is theoretically shown that the proposed scheme exactly performs maximum-likelihood( ML) decoding,which means the decoding performance is optimal. Moreover,an efficient implementation method of the proposed scheme is designed based on Viterbi algorithm. Simulation results show that the performance of the proposed soft-decision ML decoding scheme is significantly improved compared with the traditional hard-decision decoding method at the expense of moderate complexity increase.

An Adaptive Joint Source/Channel Coding Using Error Correcting Arithmetic Codes

An approximately optimal adaptive arithmetic coding (AC) system using a forbidden symbol (FS) over noisy channels was proposed which allows one to jointly and adaptively design the source decoding and channel correcting in a single process, with superior performance compared with traditional separated techniques. The concept of adaptiveness is applied not only to the source model but also to the amount of coding redundancy. In addition, an improved branch metric computing algorithm and a faster sequential searching algorithm compared with the system proposed by Grangetto were proposed. The proposed system is tested in the case of image transmission over the AWGN channel, and compared with traditional separated system in terms of packet error rate and complexity. Both hard and soft decoding were taken into account.

A WYNER-ZIV VIDEO CODING METHOD UTILIZING MIXTURE CORRELATION NOISE MODEL

In Wyner-Ziv (WZ) Distributed Video Coding (DVC), correlation noise model is often used to describe the error distribution between WZ frame and the side information. The accuracy of the model can influence the performance of the video coder directly. A mixture correlation noise model in Discrete Cosine Transform (DCT) domain for WZ video coding is established in this paper. Different correlation noise estimation method is used for direct current and alternating current coefficients. Parameter estimation method based on expectation maximization algorithm is used to estimate the Laplace distribution center of direct current frequency band and Mixture Laplace-Uniform Distribution Model (MLUDM) is established for alternating current coefficients. Experimental results suggest that the proposed mixture correlation noise model can describe the heavy tail and sudden change of the noise accurately at high rate and make significant improvement on the coding efficiency compared with the noise model presented by DIStributed COding for Video sERvices (DISCOVER).

Noise Feedback Coding Revisited:Refurbished Legacy Codecs and New Coding Models

Noise feedback coding （NFC） has attracted renewed interest with the recent standardization of backward-compatible enhancements for ITU-T G.711 and G.722. It has also been revisited with the emergence of proprietary speech codecs, such as BV16, BV32, and SILK, that have structures different from CELP coding. In this article, we review NFC and describe a novel coding technique that optimally shapes coding noise in embedded pulse-code modulation （PCM） and embedded adaptive differential PCM （ADPCM）. We describe how this new technique was incorporated into the recent ITU-T G.711.1, G.711 App. III, and G.722 Annex B （G.722B） speech-coding standards.

Integrated Joint Source-Channel Symbol-by-Symbol Decoding of Variable-Length Codes Using 3-D MAP Sequence Estimation

Most of multimedia schemes employ variable-length codes （VLCs） like Huffman code as core components in obtaining high compression rates. However VLC methods are very sensitive to channel noise. The goal of this paper is to salvage as many data from the damaged packets as possible for higher audiovisual quality. This paper proposes an integrated joint source-channel decoder （I-JSCD） at a symbol-level using three-dimensional （3-D） trellis representation for first-order Markov sources encoded with VLC source code and convolutional channel code. This method combines source code and channel code state-spaces and bit-lengths to construct a two-dimensional （2-D） state-space, and then develops a 3-D trellis and a maximum a-posterior （MAP） algorithm to estimate the source sequence symbol by symbol. Experiment results demonstrate that our method results in significant improvement in decoding performance, it can salvage at least half of （50%） data in any channel error rate, and can provide additional error resilience to VLC stream like image, audio, video stream over high error rate links.